Polarized endomorphisms of Fano varieties with complements

Abstract

Let $X$ be a Fano type variety and $(X,\Delta )$ be a log Calabi-Yau pair with $\Delta$ a Weil divisor. If $(X,\Delta )$ admits a polarized endomorphism, then we show that $(X,\Delta )$ is a finite quotient of a toric pair. Along the way, we prove that a klt Calabi-Yau pair $(X,\Delta )$ with standard coefficients that admits a polarized endomorphism is the quotient of an abelian variety.

19 pages. v2: Section 5 and examples revised